149 research outputs found
Zenoness for Timed Pushdown Automata
Timed pushdown automata are pushdown automata extended with a finite set of
real-valued clocks. Additionaly, each symbol in the stack is equipped with a
value representing its age. The enabledness of a transition may depend on the
values of the clocks and the age of the topmost symbol. Therefore, dense-timed
pushdown automata subsume both pushdown automata and timed automata. We have
previously shown that the reachability problem for this model is decidable. In
this paper, we study the zenoness problem and show that it is EXPTIME-complete.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
Binary reachability of timed-register pushdown automata and branching vector addition systems
Timed-register pushdown automata constitute a very expressive class of automata, whose transitions may involve state, input, and top-of-stack timed registers with unbounded differences. They strictly subsume pushdown timed automata of Bouajjani et al., dense-timed pushdown automata of Abdulla et al., and orbit-finite timed-register pushdown automata of Clemente and Lasota. We give an effective logical characterisation of the reachability relation of timed-register pushdown automata. As a corollary, we obtain a doubly exponential time procedure for the non-emptiness problem. We show that the complexity reduces to singly exponential under the assumption of monotonic time. The proofs involve a novel model of one-dimensional integer branching vector addition systems with states. As a result interesting on its own, we show that reachability sets of the latter model are semilinear and computable in exponential time
Timed pushdown automata revisited
This paper contains two results on timed extensions of pushdown automata
(PDA). As our first result we prove that the model of dense-timed PDA of
Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with
timeless stack. Motivated by this result, we advocate the framework of
first-order definable PDA, a specialization of PDA in sets with atoms, as the
right setting to define and investigate timed extensions of PDA. The general
model obtained in this way is Turing complete. As our second result we prove
NEXPTIME upper complexity bound for the non-emptiness problem for an expressive
subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more
restrictive subclass of PDA with timeless stack, thus subsuming the complexity
bound known for dense-timed PDA.Comment: full technical report of LICS'15 pape
Reachability analysis of first-order definable pushdown systems
We study pushdown systems where control states, stack alphabet, and
transition relation, instead of being finite, are first-order definable in a
fixed countably-infinite structure. We show that the reachability analysis can
be addressed with the well-known saturation technique for the wide class of
oligomorphic structures. Moreover, for the more restrictive homogeneous
structures, we are able to give concrete complexity upper bounds. We show ample
applicability of our technique by presenting several concrete examples of
homogeneous structures, subsuming, with optimal complexity, known results from
the literature. We show that infinitely many such examples of homogeneous
structures can be obtained with the classical wreath product construction.Comment: to appear in CSL'1
Event-Clock Nested Automata
In this paper we introduce and study Event-Clock Nested Automata (ECNA), a
formalism that combines Event Clock Automata (ECA) and Visibly Pushdown
Automata (VPA). ECNA allow to express real-time properties over non-regular
patterns of recursive programs. We prove that ECNA retain the same closure and
decidability properties of ECA and VPA being closed under Boolean operations
and having a decidable language-inclusion problem. In particular, we prove that
emptiness, universality, and language-inclusion for ECNA are EXPTIME-complete
problems. As for the expressiveness, we have that ECNA properly extend any
previous attempt in the literature of combining ECA and VPA
Analyzing Timed Systems Using Tree Automata
Timed systems, such as timed automata, are usually analyzed using their
operational semantics on timed words. The classical region abstraction for
timed automata reduces them to (untimed) finite state automata with the same
time-abstract properties, such as state reachability. We propose a new
technique to analyze such timed systems using finite tree automata instead of
finite word automata. The main idea is to consider timed behaviors as graphs
with matching edges capturing timing constraints. When a family of graphs has
bounded tree-width, they can be interpreted in trees and MSO-definable
properties of such graphs can be checked using tree automata. The technique is
quite general and applies to many timed systems. In this paper, as an example,
we develop the technique on timed pushdown systems, which have recently
received considerable attention. Further, we also demonstrate how we can use it
on timed automata and timed multi-stack pushdown systems (with boundedness
restrictions)
Adding Time to Pushdown Automata
In this tutorial, we illustrate through examples how we can combine two
classical models, namely those of pushdown automata (PDA) and timed automata,
in order to obtain timed pushdown automata (TPDA). Furthermore, we describe how
the reachability problem for TPDAs can be reduced to the reachability problem
for PDAs.Comment: In Proceedings QFM 2012, arXiv:1212.345
Revisiting Underapproximate Reachability for Multipushdown Systems
Boolean programs with multiple recursive threads can be captured as pushdown
automata with multiple stacks. This model is Turing complete, and hence, one is
often interested in analyzing a restricted class that still captures useful
behaviors. In this paper, we propose a new class of bounded under
approximations for multi-pushdown systems, which subsumes most existing
classes. We develop an efficient algorithm for solving the under-approximate
reachability problem, which is based on efficient fix-point computations. We
implement it in our tool BHIM and illustrate its applicability by generating a
set of relevant benchmarks and examining its performance. As an additional
takeaway, BHIM solves the binary reachability problem in pushdown automata. To
show the versatility of our approach, we then extend our algorithm to the timed
setting and provide the first implementation that can handle timed
multi-pushdown automata with closed guards.Comment: 52 pages, Conference TACAS 202
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